Work and Power Calculator

This calculator determines the mechanical work done by a force and the power required to perform it in a given time, fundamental concepts in physics and engineering.

Work and power formulas

The basic formulas are:

• Work: W = F × d (force times distance)
• Power: P = W / t (work per unit time)
• Alternative power: P = F × v (force times velocity)

Work is measured in joules (J), power in watts (W) and 1 watt = 1 joule/second.

Example 1: pushing an object

Problem: A force of 50 N is applied to move an object 10 m in 5 seconds.

1. Work:
   • W = 50 × 10 = 500 J.
2. Power:
   • P = 500 / 5 = 100 W.

Answer: Work = 500 J, Power = 100 W.

Example 2: lifting a load

Problem: Lift 200 kg to 3 m height in 10 seconds.

1. Force (weight):
   • F = m × g = 200 × 9.81 = 1,962 N.
2. Work:
   • W = 1,962 × 3 = 5,886 J.
3. Power:
   • P = 5,886 / 10 = 588.6 W.

Answer: Work = 5,886 J, Power = 588.6 W.

Common uses of work and power calculation

• Sizing motors and machines for specific tasks.
• Computing energy consumption of industrial processes.
• Evaluating athlete performance in strength sports.
• Designing lifting and transport systems.
• Analyzing efficiency of tools and equipment.
• Solving physics problems in education.

Common mistakes with work and power

• Not considering the angle between force and direction of motion.
• Confusing power (W) with work (J).
• Not converting units correctly (horsepower to watts: 1 hp ≈ 745.7 W).
• Forgetting that work is only done when there is displacement.

Pro tip

If the force is not parallel to the displacement, use W = F × d × cos(θ), where θ is the angle between the force and the direction of motion. When θ = 90°, the work is zero.